Rupture Process of the M 7.9 Denali Fault, Alaska, Earthquake: Subevents, Directivity, and Scaling of High-Frequency Ground Motions by Arthur Frankel

Bulletin of the Seismological Society of America, Vol. 94, No. 6B, pp. S234–S255, December 2004

Abstract Displacement waveforms and high-frequency acceleration envelopes from stations at distances of 3–300 km were inverted to determine the source process of the M 7.9 Denali fault earthquake. Fitting the initial portion of the displacement waveforms indicates that the earthquake started with an oblique thrust subevent (subevent #1) with an east–west-striking, north-dipping nodal plane consistent with the observed surface rupture on the Susitna Glacier fault. Inversion of the remainder of the waveforms (0.02–0.5 Hz) for moment release along the Denali and Totschunda faults shows that rupture proceeded eastward on the Denali fault, with two strike- slip subevents (numbers 2 and 3) centered about 90 and 210 km east of the hypocenter. Subevent 2 was located across from the station at PS10 (Trans-Alaska Pipeline Pump Station #10) and was very localized in space and time. Subevent 3 extended from 160 to 230 km east of the hypocenter and had the largest moment of the subevents. Based on the timing between subevent 2 and the east end of subevent 3, an average rupture velocity of 3.5 km/sec, close to the shear wave velocity at the average rupture depth, was found. However, the portion of the rupture 130–220 km east of the epicenter appears to have an effective rupture velocity of about 5.0 km/ sec, which is supershear. These two subevents correspond approximately to areas of large surface offsets observed after the earthquake. Using waveforms of the M 6.7 Nenana Mountain earthquake as empirical Green’s functions, the high-frequency (1– 10 Hz) envelopes of the M 7.9 earthquake were inverted to determine the location of high-frequency energy release along the faults. The initial thrust subevent produced the largest high-frequency energy release per unit fault length. The high- frequency envelopes and acceleration spectra (Ͼ0.5 Hz) of the M 7.9 earthquake can be simulated by chaining together rupture zones of the M 6.7 earthquake over distances from 30 to 180 km east of the hypocenter. However, the inversion indicates that there was relatively little high-frequency energy generated along the 60-km portion of the Totschunda fault on the east end of the rupture.

Introduction Seismograms of the 3 November 2002, M 7.9 Denali onstrated that it started as a thrust event on a northeast- fault, Alaska, earthquake provide an unprecedented oppor- striking fault, with strike-slip rupture then proceeding east- tunity to study the inner workings of a large (M Ͼ7.5) strike- ward for about 200 km along the Denali fault (Kikuchi and slip earthquake. It was recognized from geological and seis- Yamanaka, 2002). Most of the slip determined from the tele- mological observations that this earthquake involved three seismic inversion was located in an extended area centered faults: the Susitna Glacier, Denali, and Totschunda faults about 120 km east of the hypocenter. This area corresponds (Fig. 1; see Eberhart-Phillips et al., 2003). The focal mech- to the location of the highest coseismic surface offsets along anism of the event from P-wave ﬁrst motions on data from the Denali fault reported by Eberhart-Phillips et al. (2003). the local seismic network showed that it started as a thrust The switching of the rupture from the Denali fault to the subevent on a east-northeasterly striking plane (Alaska Totschunda fault, observed in coseismic offsets and after- Earthquake Information Center Web site), correlating with shock locations, was another remarkable feature of this the surface rupture reported for the Susitna Glacier fault earthquake. (Eberhart-Phillips et al., 2003). Inversion of teleseismic In this study I analyze recordings from strong-motion waveforms done shortly after the event occurred, also dem- instruments located 3 to 300 km from the rupture trace.

S234 Rupture Process of the M 7.9 Denali Fault, Alaska, Earthquake S235

Figure 1. Map showing faults involved in the 3 November 2002 M 7.9 Denali fault earthquake. Red star is epicenter. Yellow circles are aftershocks of the M 7.9 event. Green star and circles are the epicenter and aftershocks, respectively, of the M 6.7 Nenana Mountain earthquake of 23 October 2002. Stations used in this paper are shown as triangles, with colors keyed to the institutions that operate the instruments. Locations and focal mechanisms (lower-hemisphere projections) of subevents 1, 2 and 3 are shown. The oblique-thrust mechanism shown for subevent 1 was derived from ﬁtting the displacement records (see text). Sub- event 1 corresponds to rupture along the Sus- itna Glacier fault. Subevents 2 and 3 along the Denali fault were found from the inversion of waveforms.

These recordings provide substantial spatial and temporal Pipeline Pump Station #10 (PS10), 3 km from the fault trace, detail on the rupture process, at long periods (2–50 sec) and has been suggested as more possible evidence of low accel- short periods (0.1–1.0 sec). The initial results of an early erations from M Ͼ7 earthquakes (Ellsworth et al., 2004). It version of part of this work were presented in Frankel et al. is important to resolve this issue for seismic hazard studies, (2002) and Eberhart-Phillips et al. (2003). Using the dis- for constructing accurate synthetic seismograms of large placement waveforms (0.02 to 0.5 Hz), I determined the earthquakes used in engineering design, and for fundamental best-fitting mechanism of the initial subevent and then in- understanding of earthquake processes. verted the waveforms to determine the spatial and temporal The commonly observed scaling of earthquakes with history of rupture along the Denali and Totschunda faults. magnitudes less than about 6.5 indicates that the seismic There has been some question lately concerning the am- energy radiated at any given frequency E(f) is proportional plitude of high-frequency (Ͼ1 Hz) ground motions gener- to fault area A, for frequencies f above the corner frequency. ated by large earthquakes with magnitudes greater than I derive this by the following reasoning. The source spectra about 7.3, as the number of strong-motion recordings of such of such earthquakes are generally found to obey the constant 2מ large earthquakes has increased. Recordings of the M 7.4 Izmit, Turkey, and M 7.6 Chi-Chi, Taiwan, earthquakes stress drop, x model (x is the angular frequency, 2pf), 2מ show a deficit of high-frequency energy compared to pre- where the displacement spectrum u(x) has a falloff of x dictions of attenuation relations based on recordings of (acceleration spectrum is flat with respect to frequency) smaller events (Anderson et al., 2000; Somerville, 2000). above the corner frequency f0 and stress drop is uniform with Several explanations have been proposed for this apparent respect to seismic moment (e.g., Aki, 1967; Brune, 1970; deficit. The relatively modest peak acceleration of 0.36g of Hanks, 1981; Boore, 1983). In such a model, the high fre- the Denali fault earthquake recorded at the Trans-Alaska quency spectral amplitude uhf(f) at any given frequency is S236 A. Frankel

proportional to seismic moment M0 to the 1/3 power (e.g., quake was located about 25 km west of that of the Denali Frankel, 1995): fault earthquake (Fig. 1). I inverted the high-frequency (1–10 Hz) envelopes of ϰ 1/3 uhf(f) M0 . the acceleration records from the Denali fault earthquake to determine whether the high-frequency characteristics of this Now the seismic moment can be expressed as M 7.9 earthquake can be matched by stringing together the rupture zone of the M 6.7 earthquake such that it ﬁlls the ,lAu ϰ lA3/2 ס M 0 rupture area of the larger event. This inversion provides in- Ͼ where l is the shear modulus, A is fault area (pr2 for a sight on whether large earthquakes (M 7.5) are inherently circular fault with radius r), and u is average slip, which deﬁcient in high-frequency energy. is proportional to r in a constant stress drop model. This results in Data

ϰ 1/3ϰ 3/2 1/3ϰ 1/2 uhf(f) M0 (A ) A . Figure 1 shows the locations of strong-motion instruments used in this study. All of the waveforms used in this The spectrum of the radiated energy is proportional to the study were derived from accelerometers. The instruments are square of the velocity spectrum (Haskell, 1964), such that operated by several institutions. Stations at Fairbanks, Alaska, ϰ 222ϰ E(f) u˙hf(f) fu uf(f), where u˙hf (f) is the velocity spec- Geophysical Observatory (CIGO) and Valdez City Hall are ϰ 1/2 tral amplitude. Combining this with uhf (f) A from the operated by the National Strong Motion Program (NSMP)of relations above, I find that E(f) ϰ A, at any given frequency, the U.S. Geological Survey (USGS). These data were provided מ for the constant stress drop x 2 model. Hanks (1979), An- on the web site of NSMP. I used the corrected displacement drews (1981), and Frankel (1991) demonstrated that having waveforms from this web site, where the seismograms are high-pass filtered at 0.013 Hz. I chose one of the stations 2מconstant stress drop with seismic moment produces an x displacement spectral falloff. (K202) operated in Anchorage by the Geophysical Institute Many theoretical and observational studies have advo- of the University of Alaska at Fairbanks (UAF). Accelero- cated that the high-frequency energy of an earthquake is pro- grams from two stations of the Consolidated Reporting of duced by small-scale areas of high stress drop along the fault Earthquakes and Tsunamis (CREST) network, DIV and BMR, plane (Hanks, 1979; Andrews, 1981; Frankel, 1991). Here, were used. These stations are the most eastern strong-motion “high frequency” refers to frequencies above the corner fre- sites at distances less than about 500 km from the rupture quency and “small scale” denotes scale lengths less than the and provide critical constraints on the rupture process. fault dimension. For simplicity I will refer to these small- Recordings from four stations (PS9, PS10, PS11, PS12) scale areas of high stress drop as “asperities.” operated by Alyeska along the Trans-Alaska Pipeline were The observation that energy radiated at any given fre- analyzed in this study. PS10 is located only 3 km from the quency is proportional to rupture area supports the idea that trace of the Denali fault, and its recordings were critical to the number of asperities, of any given scale, is proportional this investigation. Ellsworth et al. (2004) describe their ex- to the fault area. Here I assume that asperities radiate most tensive analysis of the records from PS10 and their calibra- of their energy around a dominant frequency inversely re- tion of the instrument. The pump station records were elec- lated to their spatial extent. Having twice the rupture area tronically bandpass filtered at the site before they are would involve rupturing twice the asperities and, therefore, recorded. Ellsworth et al. (2004) and J. R. Evans (written radiating twice the energy at the dominant frequencies as- comm., 2003) calibrated the instrument at PS10 and deter- sociated with those asperities. The observed scaling that E(f) mined that it used a high-pass filter at 0.085 Hz and a low- is proportional to area also implies that any particular as- pass filter at 40 Hz. J. R. Evans (written comm., 2003) found perity radiates energy with the same amplitude and duration, that the instruments at PS9 and PS11 had similar responses, regardless of whether that asperity is part of, say, a magni- and I assumed that PS12 did also. tude 5 or a magnitude 8 earthquake. Of course, larger earth- Stations Carlo and R109 were installed by UAF person- quakes would also involve the rupture of larger asperities nel shortly after the Nenana Mountain earthquake (A. Mar- with larger slip, in addition to the smaller-scale asperities. tirosyan and U. Dutta, written comm., 2002). The hypocen- In this article, I evaluate whether the high-frequency (1– ter of the M 7.9 earthquake was located 50–60 km east of 10 Hz) ground motions of the M 7.9 Denali fault earthquake these stations. The sampling rate of the stations used in this scale so that E(f) is proportional to fault area, similar to the paper is 200 samples per second, except for stations BMR observed scaling of smaller earthquakes. The occurrence of and DIV, which have a 50 samples per second rate. the nearby M 6.7 Nenana Mountain earthquake provides important data for testing this. The Nenana Mountain earth- Modeling the Initial Subevent quake was a strike-slip event on the Denali fault that occurred on 23 October 2002, 10 days before the Denali fault I used a grid search to determine the focal mechanism earthquake. The epicenter of the Nenana Mountain earth- of the initial subevent. Synthetic seismograms for layered- Rupture Process of the M 7.9 Denali Fault, Alaska, Earthquake S237 velocity models were calculated using the frequency-wave- was largely taken from Brocher et al. (2004). This velocity number integration program of Saikia (1994). The velocity model also includes the 110-m-thick alluvium layer found models were determined by simplifying the velocity models by R. E. Kayen (written comm., 2003) at the site using sur- found in seismic refraction studies of the region. Tables 1, face-wave measurements. The velocity models for Anchor- 2, 3, 4, 5 list the velocity models. In several cases, zones age, PS11, and PS12 (Table 2), and BMR, DIV, and Valdez with velocity gradients were approximated by discrete lay- (Table 4) were simplified from models determined by Fuis ers. Generally, shear-wave velocities were determined from et al. (1991). The Fairbanks model (Table 3) was taken from P-wave velocities by dividing by 1.73, except for shallow Beaudoin et al. (1992) with a surficial alluvial layer added. layers. Surficial layers with low shear-wave velocities were I employed a velocity model for PS9 (Table 5) based on the added in most cases, to approximately account for shallow model in Brocher et al. (2004). alluvium and sediments. The PS10 velocity model (Table 1) For modeling the waveforms for initial subevent 1, I used a point source at the hypocenter with a depth of 6 km and a triangular source time function with a duration of 10 Table 1 sec. The synthetic seismograms were high-pass filtered in Velocity Model Used for PS10 the same manner as the data. I adjusted the synthetic seis-

Thickness Vp Vs Density mograms for each station to align the initial arrivals with 3 (km) (km/sec) (km/sec) (gm/cm ) Qp Qs those of the observed seismograms. This accounts for dif- 0.11 1.8 0.4 1.8 200 100 ferences between the centroid of moment release and the 0.10 2.5 1.0 2.4 400 200 hypocenter, as well as inaccuracies in the velocity models. 0.39 3.75 1.5 2.4 400 200 Approximately the first 50 sec of the displacement 0.30 5.1 2.05 2.4 400 200 4.1 5.75 3.33 2.7 400 200 waveforms at Fairbanks and Valdez and the first 80 sec of 2.0 6.0 3.47 2.7 400 200 the waveforms at Anchorage were used in the grid search. 1.0 6.17 3.57 2.7 400 200 Focal mechanisms were determined for every 5Њ increment 1.0 6.34 3.66 2.7 400 200 of strike, dip, and rake, and the resulting synthetic seismo- 1.0 6.5 3.76 2.7 400 200 grams were compared to the observed ones using the root- 30.0 6.4 3.7 2.7 400 200 7.0 6.8 3.93 2.7 400 200 mean-square residual. The best-fitting focal mechanism has 3.0 6.3 3.64 2.7 400 200 a nodal plane with a strike of 90Њ, dip of 55Њ to the north, 8.2 4.74 3.3 2000 1000 Table 4 Velocity Model Used for BMR and DIV (Valdez uses the same ס Table 2 model with 70-m surficial layer with Vs 400 m/sec added) Velocity Model Used for Anchorage, PS11, and PS12 Thickness Vp Vs Density 3 Thickness Vp Vs Density (km) (km/sec) (km/sec) (gm/cm ) Qp Qs 3 (km) (km/sec) (km/sec) (gm/cm ) Qp Qs 0.10 2.5 1.0 2.4 400 200 0.07 1.8 0.4 1.8 200 100 1.0 5.0 2.0 2.4 400 200 0.10 2.5 1.0 2.4 400 200 4.8 5.8 3.35 2.7 400 200 0.10 5.0 2.0 2.4 400 200 2.0 6.0 3.47 2.7 400 200 4.73 5.8 3.35 2.7 400 200 13.0 6.4 3.7 2.7 400 200 2.0 6.0 3.47 2.7 400 200 30.0 6.8 3.93 2.7 400 200 13.0 6.4 3.7 2.7 400 200 8.3 4.8 3.3 2000 1000 30.0 6.8 3.93 2.7 400 200 8.3 4.8 3.3 2000 1000 Table 5 Velocity Model Used for PS9 Table 3 Thickness Vp Vs Density Velocity Model Used for Fairbanks 3 (km) (km/sec) (km/sec) (gm/cm ) Qp Qs Thickness V V Density p s 0.07 1.8 0.4 1.8 200 100 (km) (km/sec) (km/sec) (gm/cm3) Q Q p s 0.10 2.5 1.0 2.4 400 200 0.07 1.8 0.4 1.8 200 100 0.73 5.1 2.05 2.4 400 200 0.10 2.5 1.0 2.4 400 200 4.1 5.75 3.33 2.7 400 200 1.83 5.4 3.12 2.7 400 200 2.0 6.0 3.47 2.7 400 200 8.0 6.0 3.47 2.7 400 200 1.0 6.17 3.57 2.7 400 200 5.0 6.1 3.53 2.7 400 200 1.0 6.34 3.66 2.7 400 200 5.0 6.25 3.61 2.7 400 200 1.0 6.5 3.76 2.7 400 200 6.0 6.4 3.7 2.7 400 200 30.0 6.4 3.7 2.7 400 200 6.0 7.1 4.1 2.7 400 200 5.0 6.8 3.93 2.7 400 200 8.2 4.74 3.3 2000 1000 8.2 4.74 3.3 2000 1000 S238 A. Frankel and rake of 115Њ (see Fig. 1). This east–west-striking, north- use a model that follows the observed fault trace in some dipping nodal plane corresponds to the general orientation spatial detail and allows for more time windows. It is essen- and sense of slip of the Susitna Glacier fault identified in the tial when modeling the waveforms at PS10, only 3 km from field (Eberhart-Phillips et al., 2003). The mechanism shows the fault trace, to use an accurate fault trace in the inversion. primarily thrusting with a minor right-lateral component, as- I am not claiming that slip occurred only at one depth suming the north-dipping nodal plane is the fault plane. This during this earthquake. I am claiming that the observed mechanism is similar to that found from P-wave first mo- waveforms can be fit by a line source that represents the tions and from the initial teleseismic analysis of Kikuchi and average depth of rupture. Since all of the stations except Yamanaka (2002), although I find that the strong-motion PS10 are located at several source depths away from the waveforms are better fit with a fault strike that is east–west faults, the depth resolution is poor along most of the fault. rather than the northeasterly strike found in the teleseismic The inversion basically follows the procedure of Hart- -Nm, zell and Heaton (1983). The seismogram at station k is de 1019 ן result. I found a best-fitting moment of 5.6 corresponding to a moment magnitude of 7.1. I denote this termined from initial thrust subevent as subevent 1. nwסnx jסFigure 2 shows the observed and predicted waveforms. i ˙ מ מ ס These waveforms include subevent 1 and later subevents uk(t) ͚͚MGij ik(t s ijT ik) * S(t), (1) ס ס along the Denali and Totschunda faults that were determined i 1 j 1 from the inversion described below. Here I will only discuss the first 50 sec or so of the records that contain subevent 1. where Mij is the seismic moment for subfault i in time win- This part of the synthetic records was derived from the best- dow j. Gik is the Green’s function between fault segment i and station k, Tik is the travel time between fault segment i fitting focal mechanism for subevent 1. ˙ For the most part, the synthetics are in good agreement and station k, and S(t) is the source time function. nx is the with the observed records. Using the mechanism for sub- number of subfaults, and nw is the number of time windows. event 1 determined by fitting stations Valdez, Fairbanks, and Each subfault is allowed to start slipping at t0 time before a Anchorage, the initial portion of the waveforms for most of rupture with velocity of vr reaches that subfault, such that the other stations also fit quite well. Subevent 1 produces מ מ xiםס the prominent initial arrivals in the waveforms at Fairbanks sij (j 1) Dt t0 , (2) and Anchorage, but the arrivals from subevent 1 are rela- vr tively small at Valdez, BMR, and DIV. Stations Carlo and

R109 recorded the waveforms only for subevent 1 and did where xi is the distance from the hypocenter and Dt is the not record the rest of the earthquake, as it ruptured away delay between each time window. from these sites. The synthetics match the large downward In the preferred inversion, I used 22 time windows start- pulse observed on the north–south records at Carlo, which ing 0.5 sec before the arrival of a rupture front with the is the largest pulse observed on any of the components. This specified rupture velocity of 3.5 km/sec. S˙(t) was a triangle downward pulse is also observed on the north–south record with a base of 1 sec. There was a 0.5 sec delay between each at R109, but its amplitude and timing are less well fit by the time window, so the triangles of S˙(t) overlap. Thus, slip was synthetics. The smaller recordings on the other components allowed to occur at any given point on the fault over a time at Carlo and R109 are not duplicated by the synthetics. Ap- of 11 sec, if necessary. No station time delays were used in parently, the velocity model may not accurately represent the inversion, unlike the modeling of subevent 1. the structure at the detail needed to match the phasing of The fault trace is taken directly from the coordinates of these relatively high-frequency records, at least at these dis- the surface rupture reported in the supplemental online ma- tances of 50–60 km. Also, there is undoubtedly more source terial from Eberhart-Phillips et al. (2003). The subfaults complexity to subevent 1 that is not contained in the point have a 3-km length, yielding 97 subfaults. The inversion is source used to make the synthetics. started at a location 22 km east of the hypocenter, corresponding to the point at which the first strike-slip surface Methodology for Inversion of Displacement offset was measured on the Denali fault. Waveforms I determine strike-slip and dip-slip components of slip on each subfault. The inversion actually solves for the mo- The remaining portions of the waveforms were inverted ments of two focal mechanisms: one with a rake of 27Њ (up- ,27Њמ to determine moment release along the Denali and Tot- ward from the horizontal) and the other with a rake of schunda faults. My approach to the inversion was to start using a positivity constraint on the moment found for each with a simple model and determine whether it could ade- focal mechanism. The strike-slip motion is constrained to be quately fit the data, before adding complexity. That is why right lateral. By allowing only positive moment values for 27Њע I used a line source at a constant depth to model the wave- each focal mechanism, the rake is allowed to vary forms. As I will show, this simple model explains the data from horizontal. This range was chosen so that the dip-slip quite well. Furthermore, using the line source allows me to moment was allowed to be as much as one-half the strike- Rupture Process of the M 7.9 Denali Fault, Alaska, Earthquake S239

Figure 2. Observed (black) displacement seismograms and synthetic (red) seismograms predicted from the ﬁt to the focal mechanism of subevent 1 and from the inversion of the remainder of the records. The seismograms are high-pass ﬁltered (see text). Note the different time scale for PS10. Numbers denote subevents associated with pulses on the observed records. Orientations of components are denoted with -up) or num ס north, U ס east, N ס letters (E bers indicating degrees clockwise from north. Seismograms start at their trigger times. (continued)

slip moment. The strike-slip and dip-slip moments for each ments. In most cases this is 0.01 to 0.013 Hz, although the subfault are determined by vector addition of the moments PS9, 10, 11, and 12 records are high-pass filtered at 0.08 Hz. of the two focal mechanisms. The number of subfaults, time The data and the Green’s functions were also low-pass fil- windows, and focal mechanisms yields 4092 unknowns to tered at 0.5 Hz. Each 3-km-long subfault is divided into nine solve for in the inversion. point sources along its length, with the Green’s functions For each fault segment, Green’s functions were calcu- shifted in time to reflect the differences in travel times and lated using the computer code of Saikia (1994) for flat- rupture timing for each point source. Travel-time differences layered velocity models. Green’s functions were determined were calculated using ray tracing. at 2-km distance increments. The synthetics were calculated The source depth is constant for all subfaults. I found with a time step of 0.25 sec, except for PS10, where I used that a source depth of 6 km provided the best fit to the seis- a time step of 0.1 sec. The synthetics were high-pass filtered mograms at PS10, which essentially constitute the only depth with the same corner frequency as the processed displace- constraint to the rupture. Depths of 3 km and 9 km were S240 A. Frankel

Figure 2. (Continued)

found to produce poorer fits to the observed records at PS10. posed of the values of Mij to be solved. The solution is I found that a dip of 80Њ to the north improved the fit to the smoothed by adding rows to the matrix to be inverted to seismograms at PS10 compared to a vertical fault, especially minimize the difference between the moments of adjacent for the vertical component. subfaults. These additional rows are described by kH where The matrix equation used in the inversion is k is a factor that controls the degree of smoothing and H is entries. The 1מ and 1ם a matrix consisting of adjacent matrix was inverted using the nonnegative least squares pro- AB ΂΃. (3) gram of Lawson and Hanson (1974). The Green’s functions ס ΂΃M kH 0 and the observed seismograms are normalized before the inversion, such that they are divided by the maximum value The matrix A is constructed from the Green’s functions for of the observed records for each station. Weights are also each subfault and time window. The vector B contains the assigned to each component. Double weight was assigned observed seismograms concatenated. The vector M is com- to the key stations of PS10, PS11, and BMR. Vertical com- Rupture Process of the M 7.9 Denali Fault, Alaska, Earthquake S241 ponents were assigned half the weight of the horizontal corresponds to M 7.0. Between 110 and 160 km east of the components. hypocenter, there are two areas of elevated moment release in the inversion result, which are labeled “a” and “b” in Results of Inversion of Displacement Waveforms Figure 3. The zone of highest moment release is found on the Many different inversions were done, using different Denali fault extending from about 160 to 230 km east of rupture velocities for the starting window, different fault the hypocenter (Fig. 3). I designate this zone as subevent 3. dips, different depths, and varying time windows. The result The moment of this subevent from the inversion is equiva- shown here represents the preferred inversion in terms of the lent to M 7.6. A similar extended zone of high moment quality of fit to the waveforms, especially to PS10. This pre- release was identified in inversions of teleseismic data by ferred inversion had the first time window starting 0.5 sec Kikuchi and Yamanaka (2002), Ji et al. (2002), and Ozacar before the arrival time of a rupture with a 3.5 km/sec et al. (2003), and in inversions of strong-motion and Global velocity. Positioning System (GPS) data by Dreger et al. (2004). Figure 3 shows the strike-slip and dip-slip moment re- There is a minor component of dip-slip motion found lease found from the preferred inversion, plotted as a func- from the inversion. The dip-slip moment is about one-sixth tion of distance along the Denali and Totschunda faults. The of the strike-slip moment, much less than was allowable distance is measured along the fault traces, using an epicen- from the rake constraint applied in the inversion. For sub- ter of 63.52Њ N, 147.53Њ W (Eberhart-Phillips et al., 2003). event 2, a small component of motion with the north side of The moment release is rather small until about 90 km east the fault down is found. Subevent 3 is also found to have a of the hypocenter. A localized zone of high strike-slip mo- minor component of north-block-down motion, which im- ment release occurs from 90 to 100 km east of the hypocen- proves the fit at BMR and other easterly stations. ter. I denote this as subevent 2. This subevent is located on The total moment found from the inversion, including Nm. Including the 1020 ן the Denali fault directly across from PS10. This subevent the dip-slip component, is 6.3 appears to be very compact along strike, with a horizontal moment found for subevent 1 yields a total moment of Nm for the Denali fault earthquake, which equals 1020 ן extent of only about 12 km. The moment of this subevent 6.8

Figure 3. Moment release per 3-km-long fault segment along the Denali and Tot- schunda faults as a function of distance along faults east of the hypocenter, derived from the inversion of displacement waveforms. Solid line is strike-slip moment release; dashed line is dip-slip moment release. The locations of subevents 2 and 3 are indicated. Also shown with arrows are the distances for PS10 and the junction of the Denali and Totschunda faults. Positive moment release for dip slip corresponds to north-side-up motion. S242 A. Frankel

M 7.9. This is identical to the moment magnitude 7.9 found waveforms at PS9 and PS11. The large arrival on PS9 103Њ from teleseismic studies (Kikuchi and Yamanaka, 2002). component is from subevent 2. The inversion matches the The observed displacement seismograms are generally amplitude and phasing of the initial arrival, but underesti- fit fairly well with the predicted waveforms from the inver- mates the ringing that follows. The inversion does not pre- sion. Figure 2 shows the synthetics from the inversion plus dict the large arrival for subevent 2 observed on the 13Њ the synthetics for subevent 1, compared with the observed component at PS9. While the inversion does duplicate the records. The synthetics are rotated into the same component arrival times and phasing of the arrivals from subevents 2 directions as the recordings. and 3 observed at PS11, the amplitudes are substantially un- The observed seismograms at PS10 are matched by the derpredicted. The large arrival at 70 sec in the 336Њ com- inversion and are dominated by subevent 2. The 317Њ component of PS11 originates from the area of moment release ponent at PS10 is 16Њ from being parallel to the local strike designated as “b” in Figure 2. Stations PS9 and PS11 are of the Denali fault, which is 121Њ. The location of this sub- located on thick alluvium. These records are higher fre- event directly across from PS10 explains how the 317Њ com- quency than most of the other stations, because of the high- ponent nearly parallel to the fault (PS10 317) has an ampli- pass filter at 0.08 Hz and because they are closer to the fault. tude similar to the 47Њ component nearly normal to the fault The poorer fits could be attributed to basin effects at periods strike. The downward S-wave first motion observed on the of about 5 sec, which would amplify the initial arrivals and 317Њ component, corresponding to motion to the southeast, cause reverberations, and possibly change the polarization is produced by right-lateral motion along the Denali fault. of the arrivals. Interestingly, the inversion predicts the ob- It is often observed that fault normal motions are larger served waveforms at PS12 quite well, which are dominated than fault parallel ones (Somerville et al., 1997). This occurs by arrivals from subevents 2 and 3. It will be useful in the when rupture is propagating toward a station and the ground future to look at the detailed velocity structure near these motions at that station are dominated by shear waves gen- stations. erated along the portion of the fault rupturing toward the Figure 4 is a map view showing the strike-slip moment station. In that situation, the polarization of the S waves release from the inversion plotted along the traces of the would be predominantly fault normal. However, this is not Denali and Totschunda faults. This plot highlights how sub- the case with PS10, since the station is so close to the fault event 2 is located directly across from PS10. Subevent 3 that its records are dominated by slip on the adjacent portion extends along the Denali fault and moment release declines of the fault. I will expand on this point later. Ellsworth et al. just before the junction between the Denali and Totschunda (2004) also concluded that the initial pulse on PS10 was pro- faults. duced on the portion of the fault across from the station. The location of subevent 2 is indicated in more detail The strong, westward, displacement pulse observed at in Figure 5, which depicts the trace of the Denali fault in the BMR was produced mostly by subevent 3, with a minor con- vicinity of PS10. The circles represent the center points in tribution from slip at “b” (Fig. 2). BMR is the station located the subfaults used in the inversion. They are offset from the in the most forward direction of the rupture, and this short- surface trace because of the 80Њ dip of the fault to the north duration, high-amplitude pulse is the classic signature of for- and the 6 km depth of the subfaults. The results of the pre- ward directivity. The large eastward pulse on the east–west ferred inversion show that subevent 2 is largely confined to records at DIV and Valdez was produced mainly by subevent the 5 subfaults colored in Figure 5. There are alternative 2, with a minor portion from moment release at “a” (Fig. 2). models that allow for more slip to the west of these subfaults, The later sizeable pulses observed on these stations were but they still require initial rupture along the portion of the generated by subevent 3. fault across from PS10. These will be discussed below. Anchorage shows a strong arrival on its east–west com- Subevent 2 occurs along a portion of the Denali fault ponent corresponding to subevent 2 (Fig. 2), with some por- where the fault strike makes a significant change, forming a tion from the moment release at “a.” The Fairbanks east– releasing bend for right-lateral strike-slip motion (Figure 5). west and north–south records also exhibit a distinct arrival The fault strike in this segment is about 15Њ greater than the from subevent 2. It is striking that Fairbanks and Anchorage fault strike in the segments to the east and west. It should do not show large arrivals from subevent 3, despite its large be noted that there are other mapped faults that intersect the moment release. Low-amplitude arrivals in the later part of Denali fault in this area. the waveforms (160 sec after the start of the record) are Given the strong influence of PS10 on the inversion, it matched by the inversion and are from subevent 3 (Fig. 2). is useful to try the inversion without using the waveforms The low amplitude of the arrivals from subevent 3 is a result at PS10 and see how well it predicts the PS10 waveforms. of rupture propagating away from these stations and the Figure 6 shows the result of the inversion without PS10. larger distance of these stations from subevent 3, compared Subevent 2 is still present and centered across from PS10, to subevent 2. Nodes in the radiation pattern for strike-slip but it is now more spread out along the strike, so that more faulting also play a role in reducing the amplitude from sub- moment release occurs west of PS10 than in the inversion event 3 for azimuths to Fairbanks and Anchorage. that used PS10. However, this extended version of subevent The inversion does a poorer job of fitting the observed 2 does not predict the waveforms observed at PS10, as shown Rupture Process of the M 7.9 Denali Fault, Alaska, Earthquake S243

Figure 4. Strike-slip moment release from the inversion (3D columns) plotted on map of Denali and Totschunda fault traces. The columns are viewed from the south. Height of each column is proportional to strike-slip moment release for that segment (subfault). Triangles are locations of PS10 and PS11. Numbers above columns are subevent numbers. Notice the localized moment release of subevent 2 near PS10 and the broader zone of moment release for subevent 3. in Figure 7. The predicted first motion at PS10 317Њ is op- about 5.0 km/sec, although a range of values could be found posite to that observed, and the predicted pulses arrive about depending on where one chooses the initial times of rupture. 5 sec earlier than the observed arrivals. This indicates that This effective rupture velocity is about 1.4 times the shear- subevent 2 is localized along the fault across from PS10. wave velocity at the rupture depth used in the inversion and Figure 8 shows the moment release from the preferred about 0.8 times the P-wave velocity. This apparent accel- inversion as a function of both distance along the fault and eration of the rupture front is constrained by the fit to the time. The diagonal lines in the plot delineate the range of strong displacement pulses from subevent 3 observed at sta- times allowed in the preferred inversion. There are interest- tions in the forward rupture direction, BMR, DIV, and Val- ing patterns of moment release in this plot. The beginning dez, and the weak arrivals from subevent 3 observed at Fair- of subevent 2 corresponds to a rupture velocity of about 3.5 banks and Anchorage. However, there may be other rupture km/sec, if we assume that the strike-slip rupture begins at models that can match these waveforms without a super- the origin time of the earthquake and at the hypocenter. The shear rupture velocity. If we take the points of moment re- 3.5 km/sec rupture velocity is similar to the 3.5 km/sec lease of subevent 2 and the east end of subevent 3 at 220 shear-wave velocity used in the velocity models for 6 km km, the average rupture velocity is about 3.5 km/sec. This depth, the source depth used in the inversion. The moment represents an average rupture velocity for the earthquake, release designated as “a” occurs in patches that rupture after implicitly including the time delay between subevent 2 and subevent 2. The moment release denoted as “b” starts with the start of subevent 3 and the accelerating rupture of sub- a delay of about 6 sec after subevent 2 and occurs about 20 event 3 found in the inversion. km to the east. It is possible that more of the energy after the first arrival The effective rupture velocity of the moment release of at PS10 is produced by rupture on the portion of the fault “b” and subevent 3 appears to accelerate to about 5.0 km/ west of PS10 than is found in the preferred inversion. If the sec as rupture proceeds between distances of 150 to 250 km start time of the slip windows are set to be 2 sec later than along the fault (Fig. 8). The rupture appears to jump ahead in the preferred inversion, the inversion result shows de- at a distance of 170 km. Taking the midpoint of the moment creased moment release of subevent 2 across from PS10 and release at “b” and the start of significant slip at the middle more moment distributed to the portion of the Denali fault of subevent 3, I estimate an effective rupture velocity of to the west of PS10. However, the fits to the PS10 waveforms S244 A. Frankel

are signiﬁcantly poorer. In either inversion, the initial portion of the pulse at PS10 comes from the area of the fault directly across from PS10. Later energy at PS10 could be from rupture between the hypocenter and subevent 2, but would have to have slower rupture velocity. The relative peak moment release of subevents 2 and 3 is dependent on having accurate Green’s functions for PS10 for close distances from the fault. If there are focusing effects from 3D variations in shear-wave velocity near PS10, this could alter the amplitude compared to the ﬂat-layered models used here. A zone of low velocity was found along the Denali fault near PS10 by Brocher et al. (2004), using seismic refraction results. Accounting for such focusing could reduce the peak moment release found for subevent 2.

Methodology for Inversion of High-Frequency Envelopes I inverted the high-frequency (1–10 Hz) envelopes of the accelerations to determine the location and strength of Figure 5. Map of fault trace near PS10, with circles indicating centers of subfaults used in the inver- high-frequency generation in the M 7.9 Denali fault earth- sion. Circles are offset to the north of surface trace quake. Here I used the model described in the Introduction, because of dip of the fault to north used in the pre- where rupture zones of the M 6.7 Nenana Mountain earth- ferred inversion and the 6-km source depth. The filled quake are strung end-to-end to fill the rupture zone of the M circles are the subfaults where the moment release of 7.9 event. I assumed that the Nenana Mountain earthquake subevent 2 is concentrated, based on the inversion. Note the location of subevent 2 directly across from ruptured the entire depth of the seismogenic zone. I esti- PS10. mated a 26-km fault length for the Nenana Mountain rupture zone using the Wells and Coppersmith (1994) empirical re- gression for surface rupture length versus magnitude for strike-slip earthquakes. The 26-km rupture length for the Nenana Mountain earthquake is similar to that found from teleseismic modeling by Kikuchi and Yamanaka (2002). Thus, the 300-km rupture length of the Denali fault earthquake was divided into 12 segments, each 26 km long. I found that using the shorter rupture length of 21 km found for the Nenana Mountain earthquake from analysis of InSAR data (Lu et al., 2003) yielded similar inversion results. The center of the first segment was placed at the hypocenter of the Denali fault earthquake. The goal of the inversion is to determine the strength of the high-frequency excitation in each of the 26-km-long segments, relative to that of the Nen- ana Mountain earthquake. Seismograms for the Denali fault earthquake for each horizontal component of each station were calculated by summing together waveforms of the Nenana Mountain earthquake recorded at that station on that component, such

that the simulated M 7.9 accelerogram u¨j (t) at station j is nxסi xiממ ס u¨j(t) ͚ SGij΂΃ t tF j ij. (4) vr 1סFigure 6. Moment release along the Denali– i Totschunda faults found from the inversion of displacement waveforms, without the PS10 waveforms. Here, S is the source factor that describes the strength of the Solid line is strike-slip moment release; dashed line i is dip-slip moment release (see caption for Fig. 3). high-frequency excitation for each fault segment i, relative Note that much of subevent 2 is now located west of to that of the Nenana Mountain earthquake. These are the PS10. parameters we solve for in the inversion of the envelopes. Rupture Process of the M 7.9 Denali Fault, Alaska, Earthquake S245

Figure 7. Observed (black) and predicted (red) displacement seismograms (high-pass ﬁl- tered) at PS10 for inversion solution done without PS10 waveforms (left) and with PS10 waveforms (right).

Gj(t) is the recorded accelerogram of the Nenana Mountain 1.0 for distances less than 100 km and 0.5 for distances earthquake at station j. Thus, the Nenana Mountain record- greater than 100 km, reflecting the transition from direct ings are used as empirical Green’s functions. xi is the dis- shear waves to Lg waves. The results of the inversion are not tance from the center of each segment to the M 7.9 epicenter. sensitive to reasonable changes in Q, f, or geometrical tj is a delay time used to align the observed and simulated spreading exponent. records. Fij is the factor needed to adjust the amplitude of Note that I do not correct for radiation pattern differ- the Nenana Mountain earthquake to the distance between the ences between the Green’s function event and the Denali fault segment i and station j. This factor includes a geomet- fault earthquake. I found that using such a correction in the rical spreading correction and a correction for attenuation, inversion caused poorer fits to the observed envelopes, in- such that dicating that radiation pattern is not strongly affecting the acceleration envelope amplitudes at 1–10 Hz for this earth- c quake. מ R0j pf(t0jijt )/Q ס Fij ΂΃e . (5) The procedure for the nonlinear inversion to determine Rij Si that best fit the observed envelopes is as follows. An initial ס model with Si 1 is used to produce a set of initial accel- Roj is the distance between the Nenana Mountain hypocenter eration seismograms u¨j(t). The final results do not depend and station j; Rij denotes the distance between fault segment on the initial values of Si. Simulated seismograms are con- i and station j; t0i is the S-wave travel time between the structed using equation (4), based on a specified rupture ve- Nenana Mountain hypocenter and station j; and tij is the S- locity Vr. The seismograms are then bandpass filtered be- wave travel time between fault segment i and station j. The tween 1 and 10 Hz, enveloped, and the envelopes smoothed frequency f is the average frequency of the bandpass-filtered with a Gaussian function. This is the same procedure applied seismogram, taking into account the fall-off of the acceler- to filter, envelope, and smooth the observed accelerograms. ation spectra with increasing frequency. I chose an average In each iteration, the change in the simulated envelope Ej(t) frequency of 3 Hz. A Q value of 340 at 3 Hz was used, based at each time t for each station j is calculated for a unit change ץ ץ on McNamara’s (2000) determinations of Q of Lg waves in in each Si, yielding estimates ofEji(t)/ S . These partial de- Alaska. c is the geometrical spreading exponent, taken to be rivatives are then used in a set of equations: S246 A. Frankel

Figure 8. Strike-slip moment release from the preferred inversion plotted as a function of distance east of the epicenter and time after the earthquake origin time. The solid black diagonal lines are the limits of the allowed solution. The slopes of these lines correspond to a rupture velocity of 3.5 km/sec and the allowed duration of slip at any given location is 10.5 sec. Note the concentrated moment release in space and time of subevent 2. Note the acceleration of rupture of subevent 3 from about 3.5 km/ sec (at 120–160 km distance) to about 5.0 km/sec (160–250 km distance).

ץ of this writing. This amplification factor was estimated by מ ס (Ej(t (DSijobs (t) pred j(t), (6 ץ Si trying different factors and assessing the fit of the simulated PS11 envelopes to the observed ones. I found that an ampli- where DSi are the adjustments to Si needed to reduce the fication factor of 4 between PS11 and PS9 gave a satisfactory residuals between the observed envelopes obsj(t) and the fit to the observed envelope amplitudes at PS11. predicted envelopes predj(t) derived from summing the em- In practice, I produced individual envelopes for each pirical Green’s functions (equation 4). A matrix is formed horizontal component. Thus, to simulate the east–west en- ץ ץ from the estimates ofEji(t)/ S , and the values of DSi are velope at BMR for the Denali fault earthquake, I summed solved for by inverting the matrix. The values of Si are then the east–west seismograms recorded at BMR for the Nenana updated, new simulated seismograms and envelopes are pro- Mountain earthquake. Of course we would expect the par- duced, new residuals are calculated, and the procedure is ticle motions to differ between the Nenana Mountain re- repeated until the residuals are no longer reduced signifi- cordings and arrivals from different portions of the Denali– cantly. This usually takes only about five iterations. If any Totschunda faults. The use of both horizontal components of the updated values of Si are less than zero, they are set to provides a guide to the variability of the results. zero for the beginning of the next iteration. Fourteen envelopes were fit in the inversion: the two Station PS11 did not record the Nenana Mountain earth- horizontal components at stations BMR, DIV, VAL, Anchor- quake, so it was necessary to use the waveforms at PS9 for age, Fairbanks, PS11, and PS9. Stations BMR, DIV, VAL, and the Nenana Mountain earthquake for substitute Green’s PS11 are particularly important because they recorded large functions for PS11. The amplitude of the waveforms had to arrivals from subevent 3. The recordings from Anchorage be adjusted for the ratio of the 1–10-Hz site response be- and Fairbanks provide more constraint on the strength of tween PS9 and PS11, which has not been studied at the time subevent 1. I found that inverting just the records from sta- Rupture Process of the M 7.9 Denali Fault, Alaska, Earthquake S247 tions that showed clear arrivals from subevent 3 (BMR, DIV, From 26 to 182 km east of the epicenter, the inversion VAL, and PS11) did not significantly change the inversion shows source factors between 0.83 and 1.3 (Fig. 9; Table 6), results for the high-frequency excitation along the Denali which indicates that the high-frequency energy radiated per and Totschunda faults. unit fault length over this portion of the Denali fault during the M 7.9 earthquake is similar to that for the M 6.7 Nenana Mountain earthquake In other words, the high-frequency Results for Inversion of High-Frequency Envelopes envelopes can be explained by stringing together Nenana Mountain ruptures. This result shows that high-frequency Figure 9 shows the high-frequency source factors for ground motions radiated by this 156-km-long portion of the the 12 segments used, from the inversion with a rupture ve- Denali rupture scale in the same manner as observed for locity of 3.0 km/sec (also see Table 6). This rupture velocity smaller earthquakes. This implies that this portion of the produced the best overall fit to the observed envelopes. A Denali fault was not deficient in high-frequency radiation, faster rupture velocity of 3.5 km/sec predicts envelopes at at least compared to the M 6.7 Nenana Mountain earthquake. PS11 that are larger in their initial portion than their later Of course, it is possible that both earthquakes may be defi- portion, which is not observed (discussed subsequently). It cient in high-frequency energy compared to an average from is possible that the actual rupture velocity for the high- other earthquakes (see Discussion). frequency radiation changes along the fault, but this would From 208 to 286 km east of the epicenter the inversion not be resolvable with the available configuration of stations. shows relatively small source factors ranging between 0 and The initial fault segment has the largest high-frequency 0.22 (Fig. 9; Table 6). These segments radiate less high- excitation of any of the segments, equal to 2.0 times the frequency energy per unit rupture length than the Nenana Nenana Mountain earthquake (Fig. 9; Table 6). This is as- Mountain earthquake. The location where the high-frequency sociated with rupture on the Susitna Glacier fault. The large source factors drop off in the inversion result is sensitive to high-frequency excitation of this thrust subevent is consis- the rupture velocity applied in the inversion. Using a faster tent with observations from other earthquakes. It is generally rupture velocity of 3.5 km/sec moves the drop-off point to observed that thrust earthquakes produce larger peak accel- about 206 km east of the epicenter. However, this faster erations and high-frequency response values than strike-slip rupture velocity yields poorer fits to the observed envelopes, or normal earthquakes with similar magnitudes (e.g., Boore as mentioned above. The resolution of the inversion is dis- et al., 1997; Abrahamson and Silva, 1997). cussed below.

Figure 9. High-frequency source factors determined from preferred inversion of 1– 10-Hz acceleration envelopes, plotted along a map of the traces of the Denali and Totschunda faults. The columns are viewed from the south. The height of each column is proportional to the high-frequency source factor, relative to that of the M 6.7 Nenana Mountain earthquake. This inversion result used a rupture velocity of 3.0 km/sec. S248 A. Frankel

Table 6 derestimate the directivity, causing an underestimation of the Source Factors Determined from Inversion of 1–10-Hz envelope amplitude. This is observed for stations BMR and Acceleration Envelopes DIV, but not VAL. Distance East of Epicenter Source Factor Relative to The inversion convincingly resolves that the 60-km por- (km) Nenana Mountain Earthquake tion of the Totschunda fault radiated relatively little high- 0 2.0 frequency energy (1–10 Hz), for reasonable values of aver- 26 1.3 age rupture velocity. I tested the resolution by taking the 52 1.1 source factors from the preferred inversion, setting the fac- 78 0.98 tors on the Totschunda fault to 1.0, and computing synthetic 104 0.84 envelopes. The predicted and observed envelopes are shown 130 0.86 156 1.1 in Figure 11. Here I used a faster rupture velocity of 3.5 km/ 182 0.89 sec in order to move the arrivals from the Totschunda fault 208 0.25 earlier in the records. The predicted envelopes at BMR, DIV, 234 0.13 VAL, and PS11 have much greater amplitude at later times 260 0.073 in the records than exhibited in the observed envelopes. Us- 286 0.097 ing a slower rupture velocity would make the fit even worse. I did find that a good fit to the duration and amplitude Figure 10 shows the observed and predicted envelopes of the envelopes at BMR, DIV, and VAL could also be ob- from the preferred inversion of the 1–10-Hz envelopes. In tained with a rupture velocity of 4.5 km/sec. This inversion general, the fits to the observed envelopes are reasonable, yielded relatively uniform source factors from 26–286 km especially considering the coarseness of the fault segmen- along the fault and source factors of about 0.6 along the tation used in the inversion. The durations of the observed Totschunda fault. However, this fast rupture velocity pro- envelopes at BMR, DIV, VAL, and PS11 are matched by the duced envelopes that decayed much faster than the observed predicted envelopes. The predicted envelope amplitudes are envelopes at PS9 and PS11. Such a fast average rupture ve- somewhat lower than the observed ones at BMR and DIV, locity from the hypocenter is not observed in the inversion and somewhat higher at Valdez (VAL). The predicted en- of the displacement records. A 4.5 km/sec rupture velocity velopes at PS11 are flat between 40 and 80 sec, approximat- would move the center of subevent 3 to the Totschunda fault, ing the overall character of the observed ones. However, the violating the surface offset observations. Since some of the predicted envelopes at PS11 do not capture the peak in the peaks of the envelopes are correlated in time with long- observed envelopes at 70 sec that is correlated with the large period pulses in the displacement records (e.g., PS11 and arrival in the displacement records at the same time (see PS11 BMR), I think it is unlikely that the source of the high- 336Њ component in Fig. 2). The inversion of the displace- frequency radiation is rupturing at such a different average ment records showed that this peak comes from the moment rupture velocity than the source of the low-frequency mo- release at “b” (Fig. 2). As apparent in Figure 8, the timing ment release. of the moment release at “b” translates into a rupture velocity Figure 12 shows observed and predicted acceleration of about 3.0 km/sec, when measured from the hypocenter to spectra from the preferred inversion for stations BMR and the center of “b.” This explains why the preferred rupture VAL. Here I have used a time window of 200 sec for BMR velocity of the high-frequency inversion is lower than the and 100 sec for Valdez, because of its shorter record. The average rupture velocity of the preferred inversion of the predicted spectra are derived from the simulated accelero- displacement waveforms. Using a higher rupture velocity grams calculated from equation (4) using the source factors (3.5 or 4.5 km/sec) in the envelope inversion causes the pre- from the preferred inversion (Table 6). There is remarkably dicted envelope at PS11 to be largest at about 50 sec and to good agreement between the amplitude and shape of the pre- decline in amplitude by 70 sec, contradicting the observa- dicted and observed spectra for frequencies above 0.5 Hz. tions. The predicted envelopes at PS9 appear to decay more The predicted spectrum overlies the observed spectrum at rapidly than the observations. This is likely caused by the VAL and contains the 1.1-Hz site resonance and the details of coarse segment spacing in the model. the scalloping that are present in the observed spectrum. The Some of the discrepancies in the predicted and observed predicted spectrum at BMR captures the shape of the spectrum envelopes are expected from the simple summation model above 0.5 Hz, but underestimates the amplitude by about used here. The waveforms of the Nenana Mountain earth- 20%. The correlation in the spectral shapes between the ob- quake may contain its directivity effects. The westward lo- served and predicted spectra attests to the fact that the spectral cation of the aftershocks relative to the hypocenter indicate shapes are dominated by site response, which is equally af- that rupture of this earthquake may have been directed more fecting the recordings from the M 6.7 and M 7.9 earthquakes. to the west. Furthermore, for stations in the direction of rup- Of course, the predicted spectra derived from summing ture propagation of the Denali fault earthquake relative to the Nenana Mountain acceleration records do not contain all the hypocenter (BMR, DIV, VAL), we would expect that us- of the low-frequency (Ͻ0.5 Hz) energy of the M 7.9 earth- ing a point source for each segment would somewhat un- quake. This is where the larger slip of the M 7.9 earthquake Rupture Process of the M 7.9 Denali Fault, Alaska, Earthquake S249

Figure 10. Observed (black) and predicted (red) smoothed envelopes for the 1–10-Hz ﬁltered acceleration records. The predicted envelopes are derived from the source factors from the inversion of the envelopes. (continued) comes into play. The M 7.9 earthquake involves larger areas quakes with source strengths derived from the high- of moment release (subevent 3) and much larger slip than frequency inversion. The frequency below which the ob- that which occurred during the Nenana Mountain earth- served and predicted spectra differ, about 0.3–0.4 Hz, quake, producing much higher moment than would be signiﬁes the corner frequency of the Nenana Mountain earth- produced from summing together Nenana Mountain earthquake. S250 A. Frankel

Figure 10. (Continued)

Comparison with Geologic and Geodetic Data event 2 does not create a surfeit of high-frequency energy, although it is so prominent in the displacement waveforms. The moment release pattern determined from the inver- This is consistent with the relatively low accelerations ob- sion of the displacement records has strong similarities to served at PS10. There is relatively little high-frequency en- the distribution of coseismic surface displacements observed ergy generated along the Totschunda fault, although there in the field reported in Eberhart-Phillips et al. (2003; see was about 1.5 m average coseismic slip on this fault ob- Fig. 13). Here I am comparing the strike-slip values along served on the surface. It is possible that the eastern portion the Denali and Totschunda faults. Subevent 2 occurs where of subevent 3 (200–230 km east of the hypocenter) also was the surface offsets notably increase to about 5 m, compared deficient in high-frequency radiation. The preferred inver- to the minor strike-slip offsets observed between the hypo- sion shows this result, although using a faster average rup- center and subevent 2. The zone of surface offsets greater ture velocity of 3.5 km/sec would move the drop-off point than 6 m observed from 160 to 230 km corresponds to the zone of highest moment release found in the inversion. The of the source factor to approximately the junction of the largest surface offsets of about 8–9 m are located along Denali and Totschunda faults. Note that the small peak in the same portion of the fault as the peak of moment release the high-frequency source factor at 160-km distance corre- found for subevent 3 by the inversion. sponds to the higher moment release at “b.” The distinct Њ In general, the geologic offsets show north-side-up dis- arrival in the displacement records at PS11 336 at 70 sec placement, which differs from the north-side-down motions (Fig. 2) is also observed in the high-frequency acceleration found from the inversion. However, the dip-slip component envelopes. found in the inversion may not always be significant. The GPS data have been inverted to determine the distribu- dip-slip component of subevent 3 improves the fits to the tion of slip along the fault planes (Hreinsdo´ttir, Freymueller, seismograms, but, given uncertainties in Green’s functions, and Burgmann, 2003; Hreinsdo´ttir, Freymueller, Fletcher, this improvement may not be robust. et al., 2003). Some of the details of these inversions have The high-frequency inversion results differ from the changed as more data were analyzed. The general charac- patterns from the low-frequency inversion and the coseismic teristics of the geodetic solutions are similar to those from offsets. Figure 13 shows the source factors from the pre- the inversion of the displacement seismograms. The geodetic ferred high-frequency (1–10 Hz) inversion, not including the results of Hreinsdo´ttir, Freymueller, and Burgmann (2003) first segment corresponding to the Susitna Glacier fault. Sub- and Hreinsdo´ttir, Freymueller, Fletcher, et al. (2003) show Rupture Process of the M 7.9 Denali Fault, Alaska, Earthquake S251

Figure 11. Observed (black) and predicted (red) envelopes, when the source factors along the Tot- schunda fault are ﬁxed at 1.0 and the source factors of the other segments are set at the values found from the inversion. A 3.5 km/sec rupture velocity was used. This ﬁgure shows that, if the Totschunda fault did radiate high-frequency similar to the Nenana Moun- tain event, it would produce longer duration envelopes than observed, for reasonable average rupture velocities similar to those found in the displacement waveform inversion.

Discussion the largest slip where subevent 3 is found from the seismic inversion. The latest results described by Hreinsdo´ttir, Frey- The results of this work highlight differences between mueller, and Burgmann (2003) have a small area of high the sources of low-frequency (0.02–0.5 Hz) and high- moment release near the location of subevent 2 from the frequency (1–10 Hz) energy radiated during the Denali fault seismic inversion. earthquake. Areas of high moment release do not necessary S252 A. Frankel

Figure 12. Observed (black) acceleration spectra and predicted (red) acceleration spectra of the M 7.9 Denali fault earthquake using the seismograms derived from equation (4) by summing together recorded waveforms of the M 6.7 Nenana Mountain earthquake, with the high-frequency source factors found from the inversion of the envelopes. correlate with areas of large high-frequency source excita- (Plafker et al., 1993) and large cumulative offset. We might tion. For example, subevent 2 is characterized by high mo- expect that accelerations from both the Nenana Mountain ment release compared to portions of the fault to the west, and Denali fault earthquakes would be lower than those from yet does not appear to generate more high-frequency energy lower slip-rate faults. I have shown that much of the high- compared to neighboring fault segments (Fig. 13). Although frequency envelopes of the M 7.9 event can be explained by the recordings at PS10 show a modest peak acceleration of stringing together rupture zones of the M 6.7 event over a 0.36g, the peak velocity at PS10 is a formidable 180 cm/sec distance of 26–182 km along the fault. (Ellsworth et al., 2003). This high velocity, modest accel- The largest high-frequency energy per fault segment oc- eration has some similarity to observed rupture near the curred during the rupture of the Susitna Glacier thrust fault northern end of the M 7.6 Chi-Chi, Taiwan, earthquake (Ma (subevent 1). Thus, thrust subevents could be expected to et al., 2001). Brodsky and Kanamori (2001) proposed that produce the highest peak accelerations of other large com- such low accelerations accompanied by high slip velocities plex earthquakes that are composed of strike-slip and thrust may be due to lubrication of the fault by increased fluid subevents. It should be noted that the low acceleration ob- pressure. The lack of high-frequency (1–10 Hz) generation served at PS10 may not be representative of near-field ac- along the Totschunda fault is notable and indicates that por- celerations of the Denali fault earthquake. PS10 does not tions of faults had significant coseismic slip but radiated little sample subevent 3, which produced the greatest seismic mo- high-frequency energy. ment of the three subevents, nor does it sample subevent 1, The amount of high-frequency generation along faults which likely had higher near-field accelerations than sub- is likely related to a number of factors, including the geo- event 2, based on the source factors from the envelope in- logic slip rate and recurrence time of a fault (Kanamori and version. It is noteworthy that the largest landslides from the Allen, 1986), the type of faulting (thrust, strike-slip, normal), M 7.9 event were observed between subevents 1 and 2 (Harp the depth of asperities (Somerville, 2000), the type of rock et al., 2003), consistent with the large high-frequency source (Anderson et al., 2000), and the tectonic setting. It has been factors found in that location from the inversion of the en- noted that faults with large cumulative offsets have simpler velopes (Fig. 9). fault traces with fewer offsets and complications than short- The inversion of the displacement waveforms indicates offset faults (Wesnousky, 1990). Faults with large cumula- that the effective rupture velocity for subevent 3 may have tive offsets are generally faults with high geologic slip rates. been supershear. Archuleta (1984) and Bouchon et al. Such high-slip-rate faults may produce earthquakes with less (2002) presented compelling evidence for supershear rupture high-frequency energy because their rupture surfaces may velocity in the 1979 Imperial Valley, California, earthquake be smoother than those of low-offset, low-slip-rate faults. and the 1999 Izmit, Turkey, earthquake, respectively. The

High-slip-rate, short-recurrence-time faults may also be 5.0 km/sec rupture velocity (1.4 Vs) determined in the pre- weaker than low-slip-rate faults, because there is less time ferred inversion from the Denali fault earthquake is the same for healing of the fault. The Denali fault in the vicinity of as the Ί2 Vs value that Freund (1979) found theoretically for the M 7.9 event has a high slip rate of about 10 mm/yr stable crack growth at speeds between the P- and S-wave Rupture Process of the M 7.9 Denali Fault, Alaska, Earthquake S253

Figure 13. Observed horizontal coseismic offsets (top; from Eberhart-Phillips et al., 2003) compared with results of inversion for strike-slip moment release (middle) from the 0.02–0.5-Hz displacement waveforms and results of the inversion for high- frequency source factors (bottom dashed line) from the 1–10-Hz acceleration envelopes. Distance is measured along fault traces. This plot does not include the moment release and high-frequency source factors for the Susitna Glacier fault. Note the overall correspondence of subevents 2 and 3 with areas of high coseismic offsets and the small values of high-frequency source factors along the Totschunda fault. velocities. The super-shear velocity may be associated with wright (2004) found that the azimuthal variation in radiated a decrease in the generation of high-frequency energy (Fig. energy determined from teleseismic arrivals indicated a 13) at the east end of subevent 3, consistent with the theo- super-shear rupture velocity. retical work of Burridge (1979). The rupture velocity on the In conclusion, analysis of the displacement waveforms Totschunda fault is not well resolved, so it is not known and acceleration envelopes of the M 7.9 Denali fault earth- whether a high rupture velocity is the cause of its lack of quake provides insight on the rupture process of large strike- high-frequency radiation. slip earthquakes and the scaling of high-frequency ground The high rupture velocity may have enhanced the ef- motions. These results will be valuable for predicting the fects of this earthquake at large distances, such as triggered ground motions expected for large strike-slip earthquakes seismicity and seiches observed in the general direction of that will occur in more populated regions, such as a recur- rupture propagation thousands of kilometers from the hypo- rence of the 1906 San Francisco earthquake along the San center (see Eberhart-Phillips et al., 2003). Choy and Boat- Andreas fault system. S254 A. Frankel

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